Colored noise in the fractional quantum Hall effect: Duality relations and exact results

We study noise in the problem of tunneling between fractional quantum Hall edge states within a four-probe geometry. We explore the implications of the strong-weak coupling duality symmetry existent in this problem for relating the various density-density autocorrelations and cross correlations between the four terminals. We identify correlations that transform as either "odd" or "antisymmetric," or "even" or "symmetric" quantities under duality. We show that the low-frequency noise is colored and that the deviations from white noise are exactly related to the differential conductance. We show explicitly that the relationship between the slope of the low-frequency noise spectrum and the differential conductance follows from an identity that holds to all orders in perturbation theory, supporting the results implied by the duality symmetry. This generalizes the results of quantum suppression of the finite frequency noise spectrum to Luttinger liquids and fractional statistics quasiparticles. [S0163-1829(99)07227-6].